Question

AYUDA!, IDENTIDADES

*sec x / 1 + csc x = tan x / 1 + sen x

*2tan x = 1/ sec x -tan x - 1/ sec x + tan x

Answer 1

Buenos días;

sec x / (1+cosec x)=(1/cos x) / (1+1/senx)=(1/cos x) / [(sen x+ 1) / sen x]=
(senx / cos x) / (1+sen x)=tg x / (1+senx).

1/(sec x-tg x)-1/(sec x+ tg x)=
=1 /[(1/cos x) - (sen x/cos x)] - 1/[(1/cos x) + (sen x/cosx)]=
=1 / [(1-senx) / cos x] - 1/[(1+sen x) / cos x]=
=(cos x) /(1- senx)-(cos x) / (1+ senx)=
=[cos x.(1+sen x)-cos x.(1-senx)] / (1-sen²x)=
=(cos x+senx.cosx-cos x+senx.cosx) / cos².x=
=(2senx.cosx) /(cos²x)=2.sen x / cos x=2.tg x.

Un saludo.